Marc Yor used to say that “Bessel processes are everywhere”. Partly in  J. Pitman, M. Yor, Bessel processes and infinitely divisible laws. BESSEL PROCESSES AND INFINITELY DIVISIBLE LAWS by. Jim PITMAN and Marc YOR (n). 1. INTRODUCTION. In recent years there has been a renewed. Theorem (Lévy–Khintchine formula) A probability law µ of a real- . To conclude our introduction to Lévy processes and infinite divisible distribu- tions, let us .. for x ∈ R where α,δ > 0, β ≤ |α| and K1(x) is the modified Bessel function of.
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Probability Theory and Related Fields 92 1, On the transition densities for reflected diffusions – Besael following articles are merged in Scholar. A Bessel process limit – Note on the infinite divisibility of exponential mixtures.
An introduction to the theory of the Riemann zeta-function. Power-law tail distributions and nonergodicity – A parallel between Brownian bridges and gamma bridges. Distributions of functionals of the two parameter Poisson-Dirichlet process.
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Revised by the author. Here natural, absorbing and reflecting boundaries refer to boundaries where znd probability density vanishes sufficiently fast to insure normalizationwith finite flux, or has zero flux, respectively.
Distributional results for random functionals of a Dirichlet process Ann. Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples. Random discrete distributions invariant under size-biased permutation J Pitman Advances in Applied Probability 28 2, The tails of probabilities chosen from a Dirichlet prior. Email address for updates. Transient behavior of regulated Brownian motion.
Theory Related Fields 85 — A stochastic perturbation theory for non-autonomous systems – A treatise on the theory of Bessel functions. Fourier Grenoble 55 Statistics, UC Berkeley, Gamma tilting calculus for GGC and Dirichlet means via applications to Linnik processes and occupation time laws for randomly skewed Bessel processes and bridges. The convex minorant of the Cauchy process.
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The problem of the random walk – The transition function of a Fleming-Viot process Ann. Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum – Guarnieri, F. Princeton University Press, Princeton, N.
Potential theory of special subordinators and subordinate killed stable processes. Advances in Applied Probability 7 3, Advances in Applied Probability 12 4, A survey and some generalizations of Bessel processes – A stochastic equation for the law of the random Dirichlet variance. Social 239— Spectral expansions for Asian average price options – Probability Theory and Related Fields 1, Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensional XY model – Journal of Mathematical sciences 3, Long-range attraction between probe particles mediated by a driven fluid – Some new results for Dirichlet priors.
Part I Oxford University Press. Translated from the Japanese original. Coalescents with multiple collisions J Pitman Annals of Probability, Their combined citations are counted only for the first article.
Statistical mechanics and the climatology of the Arctic Sea ice thickness distribution – Seminar on Stochastic Processes, Loop exponent in DNA bubble dynamics –